In integrated circuit (IC) manufacturing, a wafer or otherwise generally round substrate passes through a number of different fabrication stages to form one or more integrated circuits thereon. The wafer is generally formed out of a semiconductor material, such as silicon, and may pass through the different stages one or more times to form multiple layers upon the wafer. Throughout the process, the wafer and layers are treated in various manners to establish one or more semiconductor modules upon the wafer. These modules can be considered the building blocks of the integrated circuits, and may also comprise other modules, sub-modules and/or elements, such as transistors, for example. A static random access memory (SRAM) cell is one type of semiconductor module, for example, that comprises a plurality of transistors as well as other types of integrated circuit elements. After the fabrication process is complete, one or more integrated circuits generally exist upon discrete sections of the wafer, known as die. The individual die can then be removed (e.g., cut) from the wafer and sold to consumers (e.g., as semiconductor “chips”).
As noted, modules are made up of elements (e.g., transistors). It can be appreciated that variations within the fabrication process can affect element characteristics. Stated another way, variations of process conditions within the different fabrication stages can have an effect on the operating parameters and resulting performance of the elements. For example, varying (e.g., increasing) a process condition such as temperature, for example, at an annealing or heating stage of the fabrication process can, for example, facilitate a change in, among other things, a level of and/or rate of diffusion of a dopant substance in an element produced by the fabrication process (e.g., enhancing the level and/or rate of diffusion), whereby an operating parameter of the element, such as a switching speed of the element, for example, is resultantly altered (e.g., accelerated).
It can be appreciated that some variations within the fabrication process, or rather some variations of process conditions at the different stages of the fabrication process, can have a substantially uniform effect upon one or more elements fabricated thereby. For example, the operating parameter of threshold voltage (Vt) of a transistor type element is a function of multiple characteristics of the transistor, such as gate oxide thickness (tox) as well as level of channel doping, for example, where gate oxide thickness and channel doping are themselves a function of one or more process conditions at one or more fabrication stages.
Gate oxide thickness may, for example, be a function of a flow rate, temperature and/or viscosity, etc. of a substance applied to a wafer in establishing a layer of gate oxide material at a particular stage of the fabrication process, for example. A change in one or more of these process conditions will likely have the same effect on the thickness of the gate oxide layer across the entirety of the wafer or any resulting variations in the thickness of the gate oxide layer across the wafer will be gradual such that there will be substantially no resulting variation in thickness among elements that are in the same proximity. Accordingly, such variations in process conditions may be referred to as global variations since they have a substantially uniform effect upon the characteristic of gate oxide thickness (tox) and the operating parameter Vt across the wafer, or at least within a module. Similarly, uniform or gradual changes in characteristics, such as tox, for example, across a wafer can be referred to as global variations, and the effect of such global variations on similar elements with a module can be approximated to be the same. Also, element parameters, such as the aforementioned component of threshold voltage Vt, that vary as a result of other global variations can likewise be referred to as global variations. Generally speaking, global variations can be monitored and the process (conditions) controlled to keep such variations within a specified range.
By way of further example, changes in the process conditions of intensity of an energy source to which a resist layer is exposed and/or length of time that the resist layer is exposed to the energy source in one or more fabrication stages, may tend to have the same effect on dimensional characteristics of similar elements, where changes in dimensional characteristics may change electrical properties or operating parameters of the elements. Similarly, changes in the process conditions of amount of time that an etching process is allowed to continue, as well as chemical composition of an etching agent utilized in the etching process can have a global effect on one or more electrical characteristics of circuit elements. Again, such global variation can be monitored and the process (conditions) controlled to limit the range of such variation.
As applied to an SRAM cell, for example, a global variation in the electrical characteristics of the elements will cause a variation in the operating parameters of the SRAM cell, such as noise margin (SNM) and trip voltage (Vtrip). Exercising control over one or more process conditions to limit the global variation of the characteristics of the circuit elements (e.g., transistors) will in turn limit the range of operating parameters (e.g., SNM and/or Vtrip) of the SRAM cell incurred from the global variation of the circuit elements. If the global variation is essentially uniform across a die, then SRAM cells on a die will have the same operating parameters as influenced by the global characteristics of the elements. However, in addition to global variation there may also be local variation that may affect resulting devices, as discussed below.
It can be appreciated that changes in some process conditions can cause operating parameters and/or element characteristics to vary from element to element within a module. Some of such variations can occur over very short distances, for example, to produce a different effect on the individual elements. With regard to channel doping, for example, some dopants vary randomly at atomic distances (known as random doping fluctuation or RDF) such that different elements within the same module can have different doping characteristics and different resulting operating parameters. Such, variations that affect individual elements differently can be referred to as local variations. Accordingly, some portion of the operating parameter of threshold voltage Vt can vary from element to element (e.g., transistor to transistor) within the same module due to local variations of levels of channel doping, for example. Such variations in element parameters resulting from local variations can also be referred to as local variations. It can thus be appreciated that element characteristics and resulting operating parameters of the elements are affected by both global and local variations where the elements are uniformly affected by the global variations but are affected on a more individual basis by the local variations.
It will be further appreciated that both global and local variations will occur with some probability distribution. For example, Vt variation from RDF is generally Gaussian. However, while the global variation can usually be monitored and limited by process control to some bound (e.g., to +/−3 sigma), local variations (e.g., from RDF) generally can not be so limited, and thus are difficult to control. The choice of fabrication process(es) can affect the magnitude of the random variations, but they can not facilitate substantial control over random variation. That is, the sigma of the local variation may be reduced but the range of variation in terms of number of sigma is still not controlled. For example, the probability for local variation may be that approximately one out of 3 million elements will be at the 5 sigma range. For an SRAM module, for example, if the failure point of a cell is at 5 sigma of a local variation, then it can be expected that approximately one out of 3 million elements (e.g., memory cells) within the module will fail from that local variation. Some modules, such as inverter chains, are not sensitive to the variation of single elements since the effect is averaged out. However, other modules, such as SRAM cells are sensitive to the variations of single elements. Thus, it would be desirable to be able to predict the impact of the (substantially uncontrollable) local variations within the environment of the (somewhat controllable) global variations to determine the robustness or reliability of an integrated circuit module, where the robustness of the module may be described in terms of a distribution of an operating parameter of the fabricated module, such as noise margin (SNM) or trip voltage (Vtrip) for an SRAM cell, for example.
In the past, parametric models for transistors have been used in circuit simulators such as SPICE. These include statistical parametric models in which the probability distribution of the parameters can be specified. The distribution for global variation and local variation can be specified separately, where the parameter value used in a circuit simulation combines a global and a local value. The local value distribution can be centered at zero so that the local distribution represents a variation around the global value. The statistical parametric models are specified to represent the measured or expected variations of the transistor characteristics that result from variations in the fabrication of the transistors. There are also routines to use circuit simulators and the statistical parametric models to predict a range of circuit performance. What is needed is an efficient way to use these tools to judge the robustness of a circuit to local random variation in the environment of the controlled global variation.